Born in 1757, in Portsmouth, Province of New Hampshire, British America,[1] Sherburne attended Harvard University, graduated from Dartmouth College in 1776 and read law in 1776.

[1] During the American Revolutionary War he served in the Continental Army as a brigade staff major.

[4] Sherburne was nominated by President Thomas Jefferson on March 22, 1804, to a seat on the United States District Court for the District of New Hampshire vacated by Judge John Pickering.

[1] Pickering was the first federal official to be removed from office through impeachment on March 12, 1804.

[6] Sherburne, who as a witness for the prosecution managers had aided the case for Pickering's removal even though the latter was insane and did not knowingly commit "high crimes and misdemeanors" on the bench,[7] himself became insane and was for all intents and purposes removed from the bench in 1826, though he continued to receive his salary until his 1830 death.